Suppose you are given two shapes with no ticks or angle markings and are asked to determine if the two shapes are congruent. How could you figure out the answer to that question? How would you prove that your answer is correct? This video demonstrates one reliable approach to determining congruence in a triangle through measurement.
As you watch this video, use the study guide to follow along if you'd like. Click the button below to download the study guide.
When showing two objects are congruent, you must show all corresponding parts are congruent. Triangles have six corresponding parts--three sides and three angles. To show these parts are congruent, we must measure them carefully. Side lengths will be measured with a ruler, and angles will be measured with a protractor. Watch the animation and follow along with the measurements on the screen. Fill in the table below with the information we find. If all six sets corresponding parts are congruent, then we know the two triangles are congruent.
We will start by measuring the longest side of each triangle. Place the first tick mark on your ruler at one end and bring the other end of the ruler against the other end point. It looks like side length AC is eight point nine centimeters on this screen. Side length DF is eight point nine centimeters as well, making these two sides congruent. Next, we will measure the middle-length sides. Side BC measures six point four centimeters, and side EF measures six point four centimeters. These two sides are congruent. The final pair of sides will be measured next. Side AB measures five point two centimeters, and side length DE measures 5.2 centimeters. These sides are congruent as well. Having three pairs of congruent sides is a very good start in showing the two triangles are congruent. Let's see if the three pairs of angles are congruent as well.
Use the protractor centered at each angle. We must rotate it so that the bottom edge is concurrent with one side of the triangle. Then we read the angle on the protractor, being careful to read the correct angle. Numbers larger than ninety on this scale are reserved for obtuse angles; whereas, numbers less than ninety should be used for acute angles. Angle A appears to be acute, so its measure must be less than ninety. It appears to be forty-five degrees. The measure of angle D is also forty-five degrees. Next we will measure angle B and angle E; they correspond with one another and appear to be obtuse angles. Their angle measures are 100 degrees each. Finally, angle C and angle F are measured. They are thirty-five degrees.
Since all six pairs of corresponding parts are congruent, we can officially now say that the triangles themselves are congruent. They are the exact same shape and size. If you wrote down the data into the table, it is very easy to see that all pairs of measurements are congruent. Feel free to practice measuring lengths and angles. It is an important skill to have while moving forward with this class. Good Luck!
Question
How do you indicate that corresponding sides and angles of a shape are congruent?
